Question

Yehudy invested $19,250 in a simple interest account. After 6 years and no additional deposits or withdrawals, the account balance was $22,957.55. Find the interest rate for the account. Round to the nearest hundredth of a percent if needed.
32.1%
1.99%
19.88%
3.21%

Answer 1

19.88

Answer 2

do u want me to tell u how i got it

Answer 3

sure

Answer 4

ok so its 6 years right?

Answer 5

Yes

Answer 6

\[22957.55/6\]

Answer 7

that gives u 3826.258

Answer 8

now you divide that by the initial amount of 19250 nd boom

Answer 9

Oh, I see. Thank you!

Answer 10

np

Answer 11

Are we sure there?

So recall the formula for simple interest

I = PRT

I = interest earned
P = principal amount
R = rate of interest
T = time in years

So if we DO have 19.88% interest rate...that would give us...

\[\large I = 19250\times .1988 \times 6 = 22961.4\]

Now remember, this is just the interest earned! so adding that to the principal we would have 42211.4 in the account...would be nice, but sadly it is incorrect

If we want to calculate the true interest rate...we use the formula

\[\large A = P(1 + rt)\]

Where A is the amount after all the interest is earned *which we are given*

So plugging everything in we would have

\[\large 22957.55 = 19250(1 + r(6))\]
Now divide both sides by 19250
\[\large 1.1926 = 1 + r(6)\]
Subtract 1 from both sides

\[\large 0.1926 = r(6)\]

and finally divide both sides by 6

\(\large r = 0.0321\) or in percent form \(\large 3.21\text{%}\)